Visible crew/equipment: Ursa throws the sewer lid at Superman sending him flying backwards into the car windshield. Watch the sewer lid carefully when Superman actually hits the windshield. You can see that the sewer lid was actually attached to a belt around his waist so that it would stay in place for the shots where he is flying backward through the air.
Visible crew/equipment: When Superman is fighting Non under the New York Streets (in the sewers), manhole covers start to jet up in the sky. When the first manhole cover shoots up you can quite clearly see the gas tube in the hole and the gas cylinder attached to the cover.
Visible crew/equipment: In the shot where Zod walks on the lake's water, there is a platform visible just under the water's surface.
Deliberate mistake: During the fight in Metropolis, General Zod is about to throw a wall part at Superman, it cuts to a street scene with people and there is a "keep clear" sign reversed, showing the film was flipped for some reason.